"Honorton's estimate required fourty-six unreported chance-level experiments for each of those in the meta-study, including those that themselves gave no significant support for the paranormal hypothesis."
Why is this at all unlikely? This is a 52 year span of time, and who knows how many times each of these (only 62) 'scientists' ran the trials or tweaked the procedure before they decided they had a set of data worth submitting. Who knows how many people looked for these phenomena, didn't find them, and gave up without submission? Even without outright fraud (which I wouldn't doubt), people lie to themselves. I've worked with scientists who had evidence that their previously obtained results were bunk and submitted them anyway... 'maybe the retest was flawed...' The significant effect that was found may just be the threshold at which an investigator needs to see (or fake) results to submit a paper. There's the answer to the question Allan originally posed...
Also, on another note, not all 'forced choice' tests are conducted in the same way. Some of them involve the person looking at the card being in the same room as the guesser, and well, it's not hard to imagine ways of getting a score above chance like that.
Why is this at all unlikely? This is a 52 year span of time
309 times 46 is 14 214, which divided by 52 equals approximately 273 unpublished studies per year. I haven't seen any figures on how many studies were conducted for e.g. a specific experimental paradigm in psychology during that time, so I can't say for certain how plausible this is or isn't. It does sound a bit high considering that parapsychology hasn't exactly been the best-funded field around, though it might have had more money in the 1930's. Does anyone have numbers?
Parapsychologists are constantly protesting that they are playing by all the standard scientific rules, and yet their results are being ignored - that they are unfairly being held to higher standards than everyone else. I'm willing to believe that. It just means that the standard statistical methods of science are so weak and flawed as to permit a field of study to sustain itself in the complete absence of any subject matter.
— Eliezer Yudkowsky, Frequentist Statistics are Frequently Subjective
Imagine if, way back at the start of the scientific enterprise, someone had said, "What we really need is a control group for science - people who will behave exactly like scientists, doing experiments, publishing journals, and so on, but whose field of study is completely empty: one in which the null hypothesis is always true.
"That way, we'll be able to gauge the effect of publication bias, experimental error, misuse of statistics, data fraud, and so on, which will help us understand how serious such problems are in the real scientific literature."
Isn't that a great idea?
By an accident of historical chance, we actually have exactly such a control group, namely parapsychologists: people who study extra-sensory perception, telepathy, precognition, and so on.
There's no particular reason to think parapsychologists are doing anything other than what scientists would do; their experiments are similar to those of scientists, they use statistics in similar ways, and there's no reason to think they falsify data any more than any other group. Yet despite the fact that their null hypotheses are always true, parapsychologists get positive results.
This is disturbing, and must lead us to wonder how many positive results in real science are actually wrong.
The point of all this is not to mock parapsychology for the sake of it, but rather to emphasise that parapsychology is useful as a control group for science. Scientists should aim to improve their procedures to the point where, if the control group used these same procedures, they would get an acceptably low level of positive results. That this is not yet the case indicates the need for more stringent scientific procedures.
Acknowledgements
The idea for this mini-essay and many of its actual points were suggested by (or stolen from) Eliezer Yudkowsky's Frequentist Statistics are Frequently Subjective, though the idea might have originated with Michael Vassar.
This was originally published at a different location on the web, but was moved here for bandwidth reasons at Eliezer's suggestion.
Comments / criticisms
A discussion on Hacker News contained one very astute criticism: that some things which may once have been considered part of parapsychology actually turned out to be real, though with perfectly sensible, physical causes. Still, I think this is unlikely for the more exotic subjects like telepathy, precognition, et cetera.